1. Mt. Olive Elementary School February 9, 2015 Joyce Bishop, Ph.D.
Math Family Night
Mt. Olive Elementary School
February 9, 2015
Joyce Bishop, Ph.D.

2. Created by: COUNCIL OF CHIEF STATE SCHOOL OFFICERS (CCSSO) &
NATIONAL GOVERNORS ASSOCIATION
The Common Core State Standards project was not initiated, created or funded by the federal government or agency. The Common Core State Standards were state led and coordinated by the heads of each state’s board of education and the Governor’s of each state.
logo taken from 2 2

3. Key Shifts Focus Coherence Rigor Rock shifts
The changes described in the Common Core can be summed up in three major shifts.
The key shifts in the CCSSM
Focus - Even when state standards become more focused, instructional materials do not because they have to cover all states.
Coherence – material was not organized so that math made sense.
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4. Mathematics: 3 Shifts
Focus: Focus strongly on the essential content for each grade.

5. Shift #1: Focus Strongly on essential content
Significantly narrow the scope of content and deepen the time and energy that is spent in the math classroom.
Focus deeply on what is emphasized in the standards, so that students gain strong foundations.
Students have more opportunity to master concepts.
I’m not sure that even the new textbooks fully embody the idea of Focus.

6. Key Areas of Focus in Mathematics
Grade
Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding
K–2
Addition and subtraction – concepts, skills, and problem solving and place value
3–5
Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving 6
Ratios and proportional reasoning; early expressions and equations 7
Ratios and proportional reasoning; arithmetic of rational numbers 8
Linear algebra
In each grade level, about 70% CC example of a linear function, so it is a natural progression to move from ratios and proportional reasoning in grade 7 to linear algebra in grade 8.

7. CCSS Domain ProgressionK 1 2 3 4 5 6 7 8 HS
Counting & Cardinality
Number and Operations in Base Ten
Ratios and Proportional Relationships
Number & Quantity
Number and Operations – Fractions
The Number System
Operations and Algebraic Thinking
Expressions and Equations
Algebra
Functions
Geometry
Measurement and Data
Statistics and Probability
Statistics & Probability
The Common Core Standards are organized into Domains, Clusters, and individual standards
In Common Core, the major areas of mathematics are organized into domains.
This diagram illustrates how the domains are distributed across the Common Core State Standards.
What is not easily seen is how a domain may impact multiple domains in future grades.
An example is K-5 Measurement and Data, which splits into Statistics and Probability and Geometry in grade 6.
Likewise, Operations and Algebraic Thinking in K-5 provides foundation Ratios and Proportional Relationships, The Number System, Expressions and Equations, and Functions in grades 6-8.
You may notice that the Cluster called Counting and Cardinality appears only in Kindergarten because we intend for students to master counting in kindergarten and develop an understanding that the last number of a count tells us how many objects there are in a group.
Notice the gap after 6th and 7th grade Ratios and Proportional Relationships. That is not because there is no more to learn about ratios and proportional relationships, but because the logical progression is to extend those ideas to linear functions, which we consider part of algebra.

8. Shift #2: Coherence: Think Across Grades, and Link to Major Topics Within Grades
Carefully connect the learning within and across grades so that students can build new understanding on foundations built in previous years.
Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.
Even though we are focusing on fewer topics at each grade, these topics are carefully chosen to build on work from previous years.

9. Progression Documents
These documents support the Common Core Standards by describing how essential mathematical concepts develop across the grades. They outline a coherent development of mathematical ideas.

10. Focus: Focus strongly where the standards focus.
Mathematics: 3 Shifts
Focus: Focus strongly where the standards focus.
Coherence: Think across grades, and link to major topics
Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application

11. Shift #3: Rigor: Balance Three Elements
The CCSSM require a balance of:
Solid conceptual understanding
Procedural skill and fluency
Application of skills in problem solving situations
Pursuit of all three requires equal intensity in time, activities, and resources

12. 3 Elements of Rigor
Conceptual Understanding – Seeing relationships among ideas and knowing why a mathematical process makes sense. Procedural Understanding – Emphasizes memorization and following specific steps. Application – Using mathematical processes to solve meaningful problems.

13. Required Fluencies in K-6
Grade
Standard
Required Fluency K
K.OA.5
Add/subtract within 5 1
1.OA.6
Add/subtract within 10 2
2.OA.2
2.NBT.5
Add/subtract within 20 (know single-digit sums from memory)
Add/subtract within 100 3
3.OA.7
3.NBT.2
Multiply/divide within 100 (know single-digit products from memory)
Add/subtract within 1000 4
4.NBT.4
Add/subtract within 1,000,000 5
5.NBT.5
Multi-digit multiplication 6
6.NS.2,3
Multi-digit division
Multi-digit decimal operations
This is some of the procedural knowledge that is considered absolutely essential.

14. Two Aspects of the Common Core Standards
Content Standards
Mathematical Practices
There are two aspects of the Common Core. So far we have addressed content standards, but the Mathematical Practices part of the Common Core may require the most far-reaching adjustments.

15. Mathematical Practices
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Another aspect of the Common Core is the Mathematical Practices. These mathematical practices define what it means to do math. The mathematical practices are possible the greatest shift of all.

16. Mathematical Practices in Kid Friendly Language
I can solve problems without giving up.
I can think about numbers in many ways.
I can explain my thinking and try to understand others’.
I can show my work in many ways.
I can use math tools and tell why I chose them.
I can work carefully and check my work.
I can use what I know to solve new problems.
I can solve problems by looking for rules and patterns.

17. Martha’s Carpeting Task
Martha was re-carpeting her bedroom, which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase?
This problem may seem familiar and we’re probably comfortable with it. We make one computation and attach a label and we’re finished. What operation is needed here? What is the mathematical idea?

18. Carpeting Task Length W i d t Area h
To solve this problem we multiply length times width to find the area.

19. Fencing Task
  Ms. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen to keep the rabbits.
If Ms. Brown’s students want their rabbits to have as much room as possible, how long would each of the sides of the pen be?
Contrast the previous problem with this one.

20. Carpeting Task
Circumference
Area

21. Fencing Task 2(1) + 2(11) = 24 A = 11 sq units 2(2) + 2(10) = 24
2(4) + 2(8) = 24
A = 32 sq units

22. Fencing Task 2(6) + 2(6) = 24 A = 36 sq units 4(4) = 16
The ideas of finding the least area and the most area lay the ground work for future work with calculus, which deals with maxima and minima. And the last question asks students to go beyond finding a single answer, and describe a general method for finding the most room. The ability to generalize is essential to algebra, where we may use a letter to represent a whole class of numbers.
This problem allows students many more opportunities to engage in those mathematical practices.

23. Fencing Task
  Ms. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen to keep the rabbits.
If Ms. Brown’s students want their rabbits to have as much room as possible, how long would each of the sides of the pen be?
How long would each of the sides of the pen be if they had only 16 feet of fencing?
How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand.
Now add two more questions. Now we ask students to relate the ideas of circumference, the distance around a figure, and area. They may need to calculate more than once to find the arrangement that will allow the rabbits the most room. The ideas of finding the least area and the most area lay the ground work for future work with calculus, which deals with maxima and minima. And the last question asks students to go beyond finding a single answer, and describe a general method for finding the most room. The ability to generalize is essential to algebra, where we may use a letter to represent a whole class of numbers.

24. What does Common Core look like in classrooms?
???

25. 10-Frames For counting Number relationships Addition to 10 Place value

26. Number Talks
Number Talks: Helping Children Build Mental Math and Computation Strategies Grades K-5
Author Sherry Parrish
Grade K
Grade 2
Grade 3
Grade 5
South Shades Crest Elementary School, Hoover, Alabama

27. Resources
Google: isbe parent resources or Illinois Common Core Resource Page Choose: Parent Resources Most helpful: Common Core Standards Overview Frequently Asked Questions My website: